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Math Help - Moment generating function

  1. #1
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    Moment generating function

    Let Y be a Standard Normal random variable.
    What is the moment generating function of Y^2?
    What is the distribution of Y^2?
    Find V(2*(Y^2) + 3)
    any help would be appreciated
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  2. #2
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    Quote Originally Posted by MatsSundin View Post
    Let Y be a Standard Normal random variable.
    What is the moment generating function of Y^2?
    What is the distribution of Y^2?
    Find V(2*(Y^2) + 3)
    any help would be appreciated
    Post #7 of this thread: http://www.mathhelpforum.com/math-he...tml#post119542

    derives the distribution of Y^2 (the notation is different of course).

    Y^2 follows a chi-square distribution of degree 1. You can either look up the moment generating function or derive it from the definition.

    Standard theorem: Var(aZ + b) = a^2 Var(Z). So Var(2Y^2 + 3) = 4 Var(Y^2).

    To get Var(Y^2) you can either look it up or derive it from E[(Y^2)^2] - (E[Y^2])^2. The required expectations can be got from the moment generating function of Y^2.
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  3. #3
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    Are you Sure?

    But Chi square is a only for gamma distributed random variables and not for standard random variables. So this couldn't work? Correct?
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  4. #4
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    Quote Originally Posted by mathlete2 View Post
    But Chi square is a only for gamma distributed random variables and not for standard random variables. So this couldn't work? Correct?
    If Y is normal then Y^2 is chi-squared. The chi-squared disribution is a special case of the gamma distribution. Read Chi-Squared Distribution -- from Wolfram MathWorld.
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